PLEASE HELP!!!! Find the solution to the inequality

The area of rectangle ABCD is 72. If point A and the midpoints of BC and CD are joined to form triangle, the area of that triang

vredina [299]

Answer:

27

Step-by-step explanation:

Name the midpoint of BC point M and the midpoint of CD point N.

Triangle ABM has the 1/4 the area of the rectangle, 18. Triangle ADN also has 1/4 the area of the rectangle, 18. Triangle CMN has 1/8 the area of the rectangle, 9. That is, of the rectangle area, ...

18 + 18 + 9 = 45

are not included in triangle AMN. So, the area of that triangle is ...

72 -45 = 27 . . . . units²

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Comment on the triangle area

The triangle created by joining the midpoint of the side of a rectangle with an opposite vertex will have the same dimension as the rectangle in one direction (L), and half the dimension of the rectangle in the other direction (W). Thus, where the rectangle area is LW, the triangle area is (1/2)(L)(1/2W) = (1/4)LW, 1/4 the area of the rectangle.

Similarly, if the midpoints of adjacent sides are joined to form a triangle, the area of that is (1/2)(1/2L)(1/2W) = (1/8)LW, or 1/8 the area of the rectangle.

3 0

2 years ago

For the polynomial f(x) = 3x^3 + 3x^2 - 13x + 12 determine the average rate of change between the two given values for x

AnnyKZ [126]

Answer:

Well plz dont delete my question I need points to get mine out

Step-by-step explanation:

4 0

2 years ago

Simplify: − (sq root)16x2 if x<0.

Sever21 [200]

Step-by-step explanation:

$- \sqrt{16 {x}^{2} } \\ = - 4x$

5 0

2 years ago

A page should have perimeter of 42 inches. The printing area within the page

Tamiku [17]

Overall dimensions of the page in order to maximize the printing area is page should be 11 inches wide and 10 inches long .

Step-by-step explanation:

We have , A page should have perimeter of 42 inches. The printing area within the page would be determined by top and bottom margins of 1 inch from each side, and the left and right margins of 1.5 inches from each side. let's assume width of the page be x inches and its length be y inches So,

Perimeter = 42 inches

⇒ $2(x+y) = 42\\x+y = 21\\y = 21-x$

width of printed area = x-3 & length of printed area = y-2:

area = $length(width)$

$area = (x-3)(y-2)\\area = (x-3)(21-x-2)\\area = (x-3)(19-x)\\area = -x^{2} + 22x -57$

Let's find $\frac{d(area)}{dx}$ :

$\frac{d(area)}{dx}$ = $\frac{d(-x^{2}+22x-57)}{dx} = -2x +22$ , for area to be maximum $\frac{d(area)}{dx}$ = 0

⇒ $-2x+22 = 0\\2x =22\\x=11 inches$

And ,

$y = 21-x\\y = 21-11\\y = 10 inches$

∴ Overall dimensions of the page in order to maximize the printing area is page should be 11 inches wide and 10 inches long .

7 0

3 years ago

The graph below shows the height an elevator travels, y, in x seconds:

ad-work [718]

9514 1404 393

Answer:

25 (ft/s)

Step-by-step explanation:

The "rate of change" is taken to mean the "rise" divided by the "run". Here, adjacent points differ in their y-value by 25 ft and their x-value by 1 second.

The rate of change is ...

rise/run = (25 ft)/(1 second) = 25 ft/second

Usually, we're just interested in the numerical value: 25.

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Additional comment

The graph is mis-labeled. It is not showing "rate of ascent." It is showing height as a function of time. The "rate of ascent" is the slope of the line on the graph, not its value.

6 0

2 years ago